IB DP Maths: AI HL复习笔记1.8.1 Eigenvalues & Eigenvectors
Characteristic Polynomials
Eigenvalues and eigenvectors are properties of square matrices and are used in a lot of real-life applications including geometrical transformations and probability scenarios. In order to find these eigenvalues and eigenvectors, the characteristic polynomial for a matrix must be found and solved.
What is a characteristic polynomial?
How do I find the characteristic polynomial?
Exam Tip
- You need to remember the characteristic equation as it is not given in the formula booklet
Worked Example
Eigenvalues & Eigenvectors
How do you find the eigenvalues of a matrix?
For this course, as the characteristic polynomial will always be a quadratic, the polynomial will always generate one of the following:
- two real and distinct eigenvalues,
- one real repeated eigenvalue or
- complex eigenvalues
How do you find the eigenvectors of a matrix?
Exam Tip
- You can do a quick check to on your calculated eigenvalues as the values along the leading diagonal of the matrix you are analysing should sum to the total of the eigenvalues for the matrix
Worked Example
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